%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO462^2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:54 AM UTC 2026
% Result : Theorem 0.24s 0.38s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 18
% Syntax : Number of formulae : 177 ( 46 unt; 0 typ; 10 def)
% Number of atoms : 1500 ( 279 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 2013 ( 363 ~; 459 |; 0 &;1106 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 257 ( 257 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 67 usr; 16 con; 0-4 aty)
% ( 76 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 502 ( 0 sgn 46 !; 0 ?; 502 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_d: $i > $i > $o ).
thf(func_def_33,type,
mbox_d: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_d: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_42,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_57,type,
sK5: $i > $i ).
thf(func_def_58,type,
sK6: $i > $i ).
thf(func_def_59,type,
sK7: $i > $i ).
thf(func_def_60,type,
sK8: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_d
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_d @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^2.ax',mbox_d) ).
thf(f35,conjecture,
mvalid @ ( mimplies @ ( mbox_d @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f36,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_d @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
thf(f40,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f41,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f44,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f45,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f47,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f62,plain,
( mbox_d
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_d @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f63,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f68,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f74,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f75,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f85,plain,
~ ( mvalid @ ( mimplies @ ( mbox_d @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f86,plain,
( ( mvalid @ ( mimplies @ ( mbox_d @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f85]) ).
thf(f95,plain,
( ( mvalid @ ( mimplies @ ( mbox_d @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) ) )
!= $true ),
inference(flattening,[],[f86]) ).
thf(f101,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f102,plain,
( ( mvalid @ ( mimplies @ ( mbox_d @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f105,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f114,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f116,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f118,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f120,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f125,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f133,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f118,f120,f116,f120,f120]) ).
thf(f134,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f125,f116,f120]) ).
thf(f136,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f114,f133,f134,f134]) ).
thf(f143,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f102,f101,f134,f105,f136,f136,f105,f105]) ).
thf(f145,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ q ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f146,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ q ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f145]) ).
thf(f147,plain,
$true != sF0,
inference(definition_folding,[],[f143,f146]) ).
thf(f149,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) )
@ q ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(iff_proxy_clausification,[],[f146]) ).
thf(f150,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $true = sF0 )
| ( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( $true = sF0 )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) )
| ( $true = sF0 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) )
| ( $true = sF0 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $true = sF0 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f161,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) )
| ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ sK2 ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
| ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ sK2 ) )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ sK3 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ( p @ sK3 )
| ~ ( rel_d @ sK1 @ sK3 ) ) )
| ( $true = sF0 )
| ( $false
= ( ( q @ sK2 )
| ~ ( rel_d @ sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
( ( $true = sF0 )
| ( $false
= ( ( q @ sK2 )
| ~ ( rel_d @ sK1 @ sK2 ) ) )
| ( $false
= ( ~ ( rel_d @ sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ( q @ sK2 )
| ~ ( rel_d @ sK1 @ sK2 ) ) )
| ( $false
= ( p @ sK3 ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( $false
= ( p @ sK3 ) )
| ( $true = sF0 )
| ( $false
= ( ~ ( rel_d @ sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( p @ sK3 ) )
| ( $false
= ( q @ sK2 ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f170,plain,
( ( $false
= ( p @ sK3 ) )
| ( $true = sF0 )
| ( $true
= ( rel_d @ sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( ( $false
= ( ~ ( rel_d @ sK1 @ sK2 ) ) )
| ( $true = sF0 )
| ( $false
= ( ~ ( rel_d @ sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f172,plain,
( ( $true = sF0 )
| ( $false
= ( q @ sK2 ) )
| ( $false
= ( ~ ( rel_d @ sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f173,plain,
( ( $true
= ( rel_d @ sK1 @ sK3 ) )
| ( $false
= ( q @ sK2 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true = sF0 )
| ( $true
= ( rel_d @ sK1 @ sK2 ) )
| ( $false
= ( ~ ( rel_d @ sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f175,plain,
( ( $true = sF0 )
| ( $true
= ( rel_d @ sK1 @ sK2 ) )
| ( $true
= ( rel_d @ sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ sK2 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ sK2 ) ) ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( ( q @ X1 )
| ~ ( rel_d @ sK1 @ X1 ) ) )
| ( $false
= ( ( q @ sK2 )
| ~ ( rel_d @ sK1 @ sK2 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $false
= ( ( q @ sK2 )
| ~ ( rel_d @ sK1 @ sK2 ) ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_d @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_d @ sK1 @ sK2 ) ) )
| ( $true = sF0 )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_d @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $false
= ( q @ sK2 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_d @ sK1 @ X1 ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( q @ sK2 ) )
| ( $true = sF0 )
| ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( rel_d @ sK1 @ sK2 ) )
| ( $true
= ( ~ ( rel_d @ sK1 @ X1 ) ) )
| ( $true
= ( q @ X1 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_d @ sK1 @ sK2 ) )
| ( $true = sF0 )
| ( ( rel_d @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f198,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
= $false )
| ( $true = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f199,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ X1 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ X1 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( p @ X1 )
| ~ ( rel_d @ sK1 @ X1 ) ) )
| ( $true
= ( ( q @ X2 )
| ~ ( rel_d @ sK1 @ X2 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( q @ X2 )
| ~ ( rel_d @ sK1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_d @ sK1 @ X1 ) ) )
| ( $true = sF0 )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_d @ sK1 @ X2 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_d @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true = sF0 )
| ( $false
= ( rel_d @ sK1 @ X2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_d @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $false
= ( rel_d @ sK1 @ X2 ) )
| ( $true = sF0 )
| ( $true
= ( q @ X2 ) ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( $true = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f208,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ X1 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) )
| ~ ( rel_d @ sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) )
| ( $true
= ( ~ ( rel_d @ sK1 @ X1 ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_d @ sK1 @ X1 ) ) )
| ( $false
= ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true = sF0 )
| ( $false
= ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $false
= ( ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) )
| ( ( rel_d @ sK1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $false
= ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) ) ) )
| ( ( rel_d @ sK1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f212]) ).
thf(f215,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true
= ( ( p @ X1 )
| ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 ) ) )
| ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( ( q @ X1 )
= $false )
| ( $true = sF0 )
| ( ( rel_d @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( $true
= ( ( q @ X1 )
| ~ ( p @ X1 ) ) )
| ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f219,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 ) ) )
| ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true = sF0 )
| ( $true
= ( q @ X1 ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f340,definition,
( spl9_1
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f344,definition,
( spl9_2
<=> ( $false
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f346,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f344]) ).
thf(f348,definition,
( spl9_3
<=> ( $false
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f350,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f348]) ).
thf(f351,plain,
( spl9_1
| spl9_2
| spl9_3 ),
inference(avatar_split_clause,[],[f169,f348,f344,f340]) ).
thf(f353,definition,
( spl9_4
<=> ( $true
= ( rel_d @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f355,plain,
( ( $true
= ( rel_d @ sK1 @ sK2 ) )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f353]) ).
thf(f356,plain,
( spl9_4
| spl9_1
| spl9_3 ),
inference(avatar_split_clause,[],[f170,f348,f340,f353]) ).
thf(f358,definition,
( spl9_5
<=> ( $true
= ( rel_d @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
thf(f360,plain,
( ( $true
= ( rel_d @ sK1 @ sK3 ) )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f358]) ).
thf(f361,plain,
( spl9_2
| spl9_5
| spl9_1 ),
inference(avatar_split_clause,[],[f173,f340,f358,f344]) ).
thf(f362,plain,
( spl9_4
| spl9_1
| spl9_5 ),
inference(avatar_split_clause,[],[f175,f358,f340,f353]) ).
thf(f364,definition,
( spl9_6
<=> ! [X1: $i] :
( ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f365,plain,
( ! [X1: $i] :
( ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f364]) ).
thf(f366,plain,
( spl9_6
| spl9_2
| spl9_1 ),
inference(avatar_split_clause,[],[f182,f340,f344,f364]) ).
thf(f367,plain,
( spl9_4
| spl9_6
| spl9_1 ),
inference(avatar_split_clause,[],[f184,f340,f364,f353]) ).
thf(f369,definition,
( spl9_7
<=> ! [X1: $i] :
( ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
thf(f370,plain,
( ! [X1: $i] :
( ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f369]) ).
thf(f381,plain,
( spl9_6
| spl9_7
| spl9_1 ),
inference(avatar_split_clause,[],[f206,f340,f369,f364]) ).
thf(f383,definition,
( spl9_10
<=> ! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( ( rel_d @ sK1 @ X1 )
= $false )
| ( ( q @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
thf(f384,plain,
( ! [X1: $i] :
( ( ( rel_d @ sK1 @ X1 )
= $false )
| ( ( q @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) )
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f383]) ).
thf(f385,plain,
( spl9_10
| spl9_1 ),
inference(avatar_split_clause,[],[f217,f340,f383]) ).
thf(f387,definition,
( spl9_11
<=> ! [X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( ( rel_d @ sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
thf(f388,plain,
( ! [X1: $i] :
( ( ( rel_d @ sK1 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f387]) ).
thf(f389,plain,
( spl9_11
| spl9_1 ),
inference(avatar_split_clause,[],[f220,f340,f387]) ).
thf(f474,plain,
~ spl9_1,
inference(avatar_split_clause,[],[f147,f340]) ).
thf(f490,plain,
( ( $true = $false )
| ( $true
= ( q @ sK3 ) )
| ~ spl9_5
| ~ spl9_6 ),
inference(constrained_superposition,[],[f365,f360]) ).
thf(f496,plain,
( ( $true
= ( q @ sK3 ) )
| ~ spl9_5
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f490]) ).
thf(f500,plain,
( ( $false
= ( q @ sK3 ) )
| ( $true = $false )
| ( $true
= ( p @ sK3 ) )
| ~ spl9_5
| ~ spl9_10 ),
inference(constrained_superposition,[],[f384,f360]) ).
thf(f507,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false
= ( q @ sK3 ) )
| ~ spl9_5
| ~ spl9_10 ),
inference(trivial_inequality_removal,[],[f500]) ).
thf(f521,plain,
( ( $true = $false )
| ( $true
= ( p @ sK3 ) )
| ~ spl9_5
| ~ spl9_6
| ~ spl9_10 ),
inference(forward_demodulation,[],[f507,f496]) ).
thf(f522,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl9_5
| ~ spl9_6
| ~ spl9_10 ),
inference(trivial_inequality_removal,[],[f521]) ).
thf(f527,plain,
( ( $true = $false )
| ~ spl9_3
| ~ spl9_5
| ~ spl9_6
| ~ spl9_10 ),
inference(forward_demodulation,[],[f522,f350]) ).
thf(f528,plain,
( $false
| ~ spl9_3
| ~ spl9_5
| ~ spl9_6
| ~ spl9_10 ),
inference(trivial_inequality_removal,[],[f527]) ).
thf(f529,plain,
( ~ spl9_3
| ~ spl9_5
| ~ spl9_6
| ~ spl9_10 ),
inference(avatar_contradiction_clause,[],[f528]) ).
thf(f545,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ~ spl9_4
| ~ spl9_7 ),
inference(constrained_superposition,[],[f370,f355]) ).
thf(f555,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl9_4
| ~ spl9_7 ),
inference(trivial_inequality_removal,[],[f545]) ).
thf(f569,plain,
( ( $true
= ( q @ sK2 ) )
| ( ( p @ sK2 )
= $false )
| ( $true = $false )
| ~ spl9_4
| ~ spl9_11 ),
inference(constrained_superposition,[],[f355,f388]) ).
thf(f574,plain,
( ( ( p @ sK2 )
= $false )
| ( $true
= ( q @ sK2 ) )
| ~ spl9_4
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f569]) ).
thf(f581,plain,
( ( $true
= ( q @ sK2 ) )
| ( $true = $false )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_11 ),
inference(forward_demodulation,[],[f574,f555]) ).
thf(f582,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl9_4
| ~ spl9_7
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f581]) ).
thf(f586,plain,
( ( $true = $false )
| ~ spl9_2
| ~ spl9_4
| ~ spl9_7
| ~ spl9_11 ),
inference(forward_demodulation,[],[f582,f346]) ).
thf(f587,plain,
( $false
| ~ spl9_2
| ~ spl9_4
| ~ spl9_7
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f586]) ).
thf(f588,plain,
( ~ spl9_2
| ~ spl9_4
| ~ spl9_7
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f587]) ).
thf(f627,plain,
( ( $true
= ( q @ sK2 ) )
| ( $true = $false )
| ~ spl9_4
| ~ spl9_6 ),
inference(constrained_superposition,[],[f365,f355]) ).
thf(f637,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl9_4
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f627]) ).
thf(f647,plain,
( ( $true = $false )
| ~ spl9_2
| ~ spl9_4
| ~ spl9_6 ),
inference(forward_demodulation,[],[f637,f346]) ).
thf(f648,plain,
( $false
| ~ spl9_2
| ~ spl9_4
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f647]) ).
thf(f649,plain,
( ~ spl9_2
| ~ spl9_4
| ~ spl9_6 ),
inference(avatar_contradiction_clause,[],[f648]) ).
cnf(s1,plain,
( spl9_1
| spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f351]) ).
cnf(s2,plain,
( spl9_1
| spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f356]) ).
cnf(s3,plain,
( spl9_1
| spl9_2
| spl9_5 ),
inference(sat_conversion,[],[f361]) ).
cnf(s4,plain,
( spl9_1
| spl9_4
| spl9_5 ),
inference(sat_conversion,[],[f362]) ).
cnf(s5,plain,
( spl9_1
| spl9_2
| spl9_6 ),
inference(sat_conversion,[],[f366]) ).
cnf(s6,plain,
( spl9_1
| spl9_4
| spl9_6 ),
inference(sat_conversion,[],[f367]) ).
cnf(s9,plain,
( spl9_1
| spl9_6
| spl9_7 ),
inference(sat_conversion,[],[f381]) ).
cnf(s10,plain,
( spl9_1
| spl9_10 ),
inference(sat_conversion,[],[f385]) ).
cnf(s11,plain,
( spl9_1
| spl9_11 ),
inference(sat_conversion,[],[f389]) ).
cnf(s32,plain,
~ spl9_1,
inference(sat_conversion,[],[f474]) ).
cnf(s37,plain,
( ~ spl9_3
| ~ spl9_5
| ~ spl9_6
| ~ spl9_10 ),
inference(sat_conversion,[],[f529]) ).
cnf(s43,plain,
( ~ spl9_2
| ~ spl9_4
| ~ spl9_7
| ~ spl9_11 ),
inference(sat_conversion,[],[f588]) ).
cnf(s47,plain,
( ~ spl9_2
| ~ spl9_4
| ~ spl9_6 ),
inference(sat_conversion,[],[f649]) ).
cnf(s52,plain,
spl9_11,
inference(rat,[],[s11,s32]) ).
cnf(s53,plain,
spl9_10,
inference(rat,[],[s10,s32]) ).
cnf(s54,plain,
( spl9_6
| spl9_7 ),
inference(rat,[],[s9,s32]) ).
cnf(s57,plain,
( spl9_4
| spl9_6 ),
inference(rat,[],[s6,s32]) ).
cnf(s58,plain,
( spl9_2
| spl9_6 ),
inference(rat,[],[s5,s32]) ).
cnf(s59,plain,
( spl9_4
| spl9_5 ),
inference(rat,[],[s4,s32]) ).
cnf(s60,plain,
( spl9_2
| spl9_5 ),
inference(rat,[],[s3,s32]) ).
cnf(s61,plain,
( spl9_3
| spl9_4 ),
inference(rat,[],[s2,s32]) ).
cnf(s62,plain,
( spl9_2
| spl9_3 ),
inference(rat,[],[s1,s32]) ).
cnf(s63,plain,
spl9_2,
inference(rat,[],[s37,s62,s60,s58,s53]) ).
cnf(s64,plain,
~ spl9_4,
inference(rat,[],[s54,s43,s47,s63,s52]) ).
cnf(s65,plain,
spl9_6,
inference(rat,[],[s57,s64]) ).
cnf(s66,plain,
spl9_5,
inference(rat,[],[s59,s64]) ).
cnf(s67,plain,
spl9_3,
inference(rat,[],[s61,s64]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s37,s53,s67,s65,s66]) ).
thf(f659,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO462^2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 % Computer : n014.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 16:58:45 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running higher-order theorem proving
% 0.24/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.38 % (2937221)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.38 % (2937232)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.38 % (2937232)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.24/0.38 % (2937229)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4176088793:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.24/0.38 % (2937232)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=792240469:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.38 % (2937227)lrs+10_16_si=on:nwc=1.5:random_seed=809481846:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.38 % (2937228)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1645773746:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.38 % (2937226)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2066751535:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.38 % (2937230)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1380083455:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.38 % (2937231)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=771360159:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.38 % (2937228)Instruction limit reached!
% 0.24/0.38 % (2937228)------------------------------
% 0.24/0.38 % (2937228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.38 % (2937228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.38 % (2937228)CaDiCaL version: 2.1.3
% 0.24/0.38 % (2937228)Termination reason: Instruction limit
% 0.24/0.38 % (2937228)Termination phase: Property scanning
% 0.24/0.38 % (2937228)Time elapsed: 0.003 s
% 0.24/0.38 % (2937228)Peak memory usage: 9 MB
% 0.24/0.38 % (2937228)Instructions burned: 3 (million)
% 0.24/0.38 % (2937232) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2937221-2937232"...
% 0.24/0.38 % (2937226) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2937221-2937226"...
% 0.24/0.38 % (2937227)Instruction limit reached!
% 0.24/0.38 % (2937227)------------------------------
% 0.24/0.38 % (2937227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.38 % (2937227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.38 % (2937227)CaDiCaL version: 2.1.3
% 0.24/0.38 % (2937227)Termination reason: Instruction limit
% 0.24/0.38 % (2937227)Termination phase: Saturation
% 0.24/0.38 % (2937227)Time elapsed: 0.017 s
% 0.24/0.38 % (2937227)Peak memory usage: 12 MB
% 0.24/0.38 % (2937227)Instructions burned: 18 (million)
% 0.24/0.38 % (2937231) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2937221-2937231"...
% 0.24/0.38 % (2937230)Instruction limit reached!
% 0.24/0.38 % (2937230)------------------------------
% 0.24/0.38 % (2937230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.38 % (2937230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.38 % (2937230)CaDiCaL version: 2.1.3
% 0.24/0.38 % (2937230)Termination reason: Instruction limit
% 0.24/0.38 % (2937230)Termination phase: Saturation
% 0.24/0.38 % (2937230)Time elapsed: 0.023 s
% 0.24/0.38 % (2937230)Peak memory usage: 11 MB
% 0.24/0.38 % (2937230)Instructions burned: 24 (million)
% 0.24/0.38 % (2937232)...printing done.
% 0.24/0.38 % (2937232)Refutation found. Thanks to Tanya!
% 0.24/0.38 % SZS status Theorem for theBenchmark
% 0.24/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.38 % (2937232)------------------------------
% 0.24/0.38 % (2937232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.38 % (2937232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.38 % (2937232)CaDiCaL version: 2.1.3
% 0.24/0.38 % (2937232)Termination reason: Refutation
% 0.24/0.38 % (2937232)Time elapsed: 0.033 s
% 0.24/0.38 % (2937232)Peak memory usage: 13 MB
% 0.24/0.38 % (2937232)Instructions burned: 36 (million)
% 0.24/0.38 % (2937221)Success in time 0.063 s
% 0.24/0.38 % Vampire exiting
%------------------------------------------------------------------------------